--- title: "Mutually exclusive, independent and contingent projects" subject: "Engineering Economics" chapter: 4 key: "semester_6/engineering_economics:mutually-exclusive-independent-contingent" source: https://www.bctengineer.com/q/semester_6/engineering_economics/mutually-exclusive-independent-contingent site: BCT Engineering --- # Mutually exclusive, independent and contingent projects Engineering Economics · Chapter 4: Comparative Analysis of Alternatives - Asked in: 2072 Asoj, 4 marks; 2070 Magh, 4 marks; 2067 Mangsir, 4 marks; 2065 Kartik, 6 marks (asked 4 times) - Video: [Combination of projects | Engineering economics numerical | 2017 PU](https://www.youtube.com/watch?v=Qk6na2Thgls) — Sudip Dhakal - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/mutually-exclusive-independent-contingent - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4 ## Question Define mutually exclusive projects, independent projects and contingent projects with proper combinations. ## Short answer Mutually exclusive: only one chosen (m+1 alternatives). Independent: no effect (2^n combinations). Contingent: acceptance depends on prerequisite project (fewer than 2^n feasible combinations). Examples: machine models, separate buildings, factory and outlet. ## Answer Projects are classified by how the choice of one affects the others. The classification decides which combinations are feasible before any economic comparison is made. #### Mutually exclusive projects Projects are mutually exclusive when choosing one rules out all the others; they perform the same function, so only one can be accepted. Example: three machine models for the same job, or three bridge designs at one site. For m mutually exclusive projects A, B, C there are m + 1 = 4 feasible alternatives: do nothing, A, B, C. #### Independent projects Projects are independent when accepting or rejecting one does not affect the cash flows or acceptance of the others. Any number may be chosen if money is available. Example: a new computer lab and a new library building. For n independent projects there are 2ⁿ combinations (including do nothing). For A, B, C: 2³ = 8. | Combination | A | B | C | |---|---|---|---| | 1 (do nothing) | 0 | 0 | 0 | | 2 | 1 | 0 | 0 | | 3 | 0 | 1 | 0 | | 4 | 0 | 0 | 1 | | 5 | 1 | 1 | 0 | | 6 | 1 | 0 | 1 | | 7 | 0 | 1 | 1 | | 8 | 1 | 1 | 1 | (1 = accepted, 0 = rejected.) With a budget limit, combinations that cost more than the budget are dropped. #### Contingent (dependent) projects A project is contingent when its acceptance depends on the acceptance of another (the prerequisite). Example: a sales outlet (B) is possible only if the factory (A) is built; a computer lab software package depends on buying the computers. If B is contingent on A (and C is independent), the feasible combinations are: | Combination | A | B | C | |---|---|---|---| | 1 | 0 | 0 | 0 | | 2 | 1 | 0 | 0 | | 3 | 1 | 1 | 0 | | 4 | 0 | 0 | 1 | | 5 | 1 | 0 | 1 | | 6 | 1 | 1 | 1 | The combinations with B but without A, (0,1,0) and (0,1,1), are infeasible, so 6 of the 8 combinations remain. #### Summary | Type | Relationship | Number of alternatives | |---|---|---| | Mutually exclusive | Only one may be chosen | m + 1 | | Independent | No effect on each other | 2ⁿ | | Contingent | One needs the other | Less than 2ⁿ | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines mutually exclusive projects? A. One needs the other B. Choosing one rules out the others C. Any combination may be chosen D. They have equal cost Answer: B. They serve the same function so only one can be accepted. (Key point: Mutually exclusive) 2. For 3 mutually exclusive projects A, B, C, how many feasible alternatives (including do nothing) exist? A. 6 B. 4 C. 8 D. 3 Answer: B. m + 1 = 4: do nothing, A, B, C. (Key point: Count of alternatives) 3. For 3 independent projects, how many combinations are there? A. 3 B. 4 C. 8 D. 6 Answer: C. 2^n = 2^3 = 8 including do nothing. (Key point: Independent combinations) 4. If B is contingent on A and C is independent, how many of the 8 combinations are feasible? A. 8 B. 6 C. 4 D. 2 Answer: B. Combinations with B but not A are infeasible, leaving 6. 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